{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:16.558953Z",
     "start_time": "2018-07-19T07:45:15.968317Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os\n",
    "from sklearn.datasets import fetch_mldata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'COL_NAMES': ['label', 'data'],\n",
       " 'DESCR': 'mldata.org dataset: mnist_original',\n",
       " 'data': array([[0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        ...,\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0],\n",
       "        [0, 0, 0, ..., 0, 0, 0]], dtype=uint8),\n",
       " 'target': array([0., 0., 0., ..., 9., 9., 9.])}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.getcwd()\n",
    "\n",
    "mnist = fetch_mldata(\"mnist_original\",data_home=path)\n",
    "mnist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = mnist['data'], mnist['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 784)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 为了机器学习方便, 讲uint型的数据转化成float\n",
    "X_train = np.array(X[:60000], dtype=float)\n",
    "y_train = np.array(y[:60000], dtype=float)\n",
    "X_test = np.array(X[60000:], dtype=float)\n",
    "y_test = np.array(y[60000:], dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 使用KNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:19.927866Z",
     "start_time": "2018-07-19T07:45:19.883890Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 55.6 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "           metric_params=None, n_jobs=1, n_neighbors=5, p=2,\n",
       "           weights='uniform')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_clf = KNeighborsClassifier()\n",
    "%time knn_clf.fit(X_train, y_train)\n",
    "# Wall time: 55.6 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 16min 7s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9688"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time knn_clf.score(X_test, y_test)\n",
    "# Wall time: 16min 7s\n",
    "# 0.9688"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA降维"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:24.518019Z",
     "start_time": "2018-07-19T07:45:24.423080Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(0.9)\n",
    "pca.fit(X_train)\n",
    "X_train_reduction = pca.transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 87)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_reduction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 908 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "           metric_params=None, n_jobs=1, n_neighbors=5, p=2,\n",
       "           weights='uniform')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_clf_pca = KNeighborsClassifier()\n",
    "%time knn_clf_pca.fit(X_train_reduction, y_train)\n",
    "# Wall time: 908 ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test_reduction = pca.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1min 46s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9728"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time knn_clf_pca.score(X_test_reduction, y_test)\n",
    "# Wall time: 1min 46s\n",
    "# 0.9728"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA的降噪效果"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 手写识别的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:29.874701Z",
     "start_time": "2018-07-19T07:45:29.869702Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:30.727174Z",
     "start_time": "2018-07-19T07:45:30.567272Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits = datasets.load_digits()\n",
    "X = digits.data\n",
    "y = digits.target\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:33.197642Z",
     "start_time": "2018-07-19T07:45:33.166660Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noisy_digits = X + np.random.normal(0, 4, size=X.shape)\n",
    "example_digits = noisy_digits[y==0, :][:10]\n",
    "\n",
    "for num in range(1,10):\n",
    "    x_num = noisy_digits[y==num, :][:10]\n",
    "    example_digits = np.vstack([example_digits, x_num])\n",
    "\n",
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:42.559840Z",
     "start_time": "2018-07-19T07:45:37.985677Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(10,10, figsize=(10,10),\n",
    "                            subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                            gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8), cmap='binary', \n",
    "                  interpolation='nearest', clim=(0, 16))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:46:46.404283Z",
     "start_time": "2018-07-19T07:46:40.650847Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d5a9cc20f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:58.842752Z",
     "start_time": "2018-07-19T07:45:58.813771Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.5, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.5)\n",
    "pca.fit(noisy_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:45:59.877111Z",
     "start_time": "2018-07-19T07:45:59.870116Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-19T07:46:06.775837Z",
     "start_time": "2018-07-19T07:46:00.775556Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24260fc3cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)\n",
    "plot_digits(filtered_digits)"
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